# Tamm Fundamentals Of The Theory Of Electricity

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- Publication date
- 1979

- Topics
- physics, science, electrodynamics, electromagnetism, maxwell' equations, electromagnetic induction, gauss law, dielectrics

- Collection
- mir-titles; additional_collections

- Language
- English

The present book is intended for persons acquainted with differential and integral calculus and with vector algebra. The fundamentals of vector analysis are set out in the text as needed. The main object of this book is to find out the physical meaning and content of the fundamental laws and postulates of the theory of electricity. In comparison with this object, only a subordinate part is relegated to formal and logical harmony, and to a strict and ordered treatment.Not trying to achieve completeness of discussion, I omitted even comparatively important questions if they dropped out of the general line of the exposition (for example, thermoelectric phenomena and electrolysis). On the other hand, I permitted myself to treat in somewhat greater detail than is usually the custom some questions (for example in the theory of dielectrics and magnetics). I did not set out technical applications of the theory, but tried as far as possible to prepare the reader to pass over directly to studying the applied theory of electricity.

The book was translated from the Russian by *G. Leib* and was first published by Mir Publishers in 1979. This is the translation of the Ninth Edition of the book.

Contents

Preface to the Ninth Russian Edition 11

From the Preface to the First Russian Edition 12

From the Preface to the Third Russian Edition 13

From the Preface to the Eighth Russian Edition 14

List of Most Important Symbols 15

Introduction 19

1.

Electric Field of Fixed Charges in the Absence of Dielectrics 23

1.1. Coulomb's Law 23

1.2. Electric Field 27

1.3. Gauss's Law 29

1.4. Electric Field of Charged Surfaces 33

1.5. Conductors in an Electric Field 38

1.6. Sources of an Electric Field. Surface Divergence 41

1.7. Work of Electric Forces. Its Independence of the Shape of the

Path. Continuity of the Tangential Components of the Vector E 45

1.8. Potential of an Electrostatic Field 50

1.9. Capacitance. Capacitors 56

1.10. Gradient of Electrostatic Potential. Lines of Force 60

1.11. Poisson and Laplace Equations 65

1.12. Potential of Space and Surface Charges 70

1.13. Typical Problems of Electrostatics 77

1.14. Electrical Double Layer 81

1.15. Energy of Interaction of Electric Charges 86

1.16. Energy of an Electric Field 90

1.17. Ponderomotive Forces 96

1.18. Determining the Ponderornotive Forces from the Expression for Energy 99

1.19. Instability of Electrical Systems. Constraints 104

2.

Dielectrics 108

2.1. Dielectrics. Electric Moment and Potential of a Neutral

Molecule. Polarization of a Dielectric 108

2.2. Free and Bound Charges. Potential of an Electric Field When

Dielectrics Are Present. Dependence of Polarization on the Field 113

2.3. Electric Displacement Vector. Differential Equations of a Field

in an Arbitrary Medium. Induction Lines 117

2.4. Electric Field in a Homogeneous Dielectric 122

2.5. Direct Calculation of a Field When a Dielectric Is Present (in

Very Simple Cases) 125

2.6. Micro- and Macroscopic Values of Physical Quantities 130

2.7. Derivation of Equations for the Field in Dielectrics by Averaging the

Microscopic Field 134

2.8. Two Classes of Dielectrics. Quasi-Elastic Dipoles 137

2.9. Difference of the Field Acting on a Dipole from the Mean One 139

2.10. Polarization of Dielectrics Whose Molecules Have a Constant

Electric Moment. Temperature Dependence of Permittivity 144

2.11. Energy of the Electric Field in Dielectrics 150

2.12. Energy Transformations Connected with the Polarization of

Dielectrics. Free Energy of an Electric Field 154

2.13. Ponderomotive Forces in Dielectrics 162

2.14. Reduction of Body Forces to Tensions 170

2.15. Stress Tensor of an Electric Field 175

3.

Steady Electric Current 184

3.1. Current in Metals. Ohm's and Joule's Laws. Voltage 184

3.2. Current Density. Differential Form of Ohm's and Joule's Laws 188

3.3. Conditions of Steadiness of Currents. Continuity

Equation. Current Filaments 191

3.4. Extraneous Electromotive Forces. Quasilinear Currents. Kirchhoff's

Second Law 195

3.5. Conversion of Energy in a Current Circuit. Contact E.M.F.'s 200

3.6. Fundamental Concepts of the Electron Theory of Metals. Tolman's Experiments 206

3.7. Electron Theory of Electrical Conductivity. Difficulties of the

Classical Theory. Sommerfeld's Theory 210

4.

Ponderomotive Interaction of Steady Currents and Their Magnetic Field

(in the Absence of Magnetizing Media) 218

4.1. The Magnetic Field of Currents 218

4.2. Interaction of Current Elemerits. The Electromagnetic Constant 222

4.3. Transition from Line Currents to Currents Having a Finite Cross

Section 226

4.4. Lorentz Force 229

4.5. Vector Potential of a Magnetic Field 234

4.6. Differential Equations of a Magnetic Field. Circulation of

Magnetic Field Intensity 239

4.7. Potential Fields and Solenoidal Fields. Comparison of

Differential Equations for an Electric and a Magnetic Fields 241

4.8. Boundary Conditions in the Magnetic Field of Currents. Surface

Currents. Surface Curl. Field of an Infinite Solenoid 242

4.9. Ponderomotive Forces Acting on a Current Loop in a Magnetic

Field. Potential Function of a Current in an External Magnetic Field 248

4.10. Ponderomotive Interaction of Currents. Mutual Induction 252

4.11. Self-Inductance. Total Potential Function of a System of

Currents 258

4.12. Magnetic Lines of Force 262

4.13. Topology of a Vortex (Magnetic) Field. Conditional Barriers 268

4.14. Magnetic Sheets. Their Equivalence' to Currents 272

4.15. Magnetic Moment of a Current. Elementary Currents and Magnetic Dipoles 278

4.16. Direct Determination of the Field of Elementary Currents and the

Forces Acting on Them 282

4.17. Evolution of Notions of the Nature of Magnetism. Spin of Electrons 290

4.18. Absolute (Gaussian) and Other Systems of Units, The

Electromagnetic Constant 294

5.

Magnetics (Magnetizable Media) 302

5.1. Magnetization of Magnetics. Molecular Currents and Conduction Currents 302

5.2. Vector Potential of a Magnetic Field in the Presence of

Magnetics. Mean Density of Space and Surface Molecular Currents 306

5.3. Differential Equations of the Macroscopic Magnetic Field in

Magnetics. Magnetic Field Intensity in Magnetics and Magnetic Induction Vector. 311

5.4. Dependence of Magnetization on Magnetic Field Intensity. Para-,

Dia-, and Ferromagnetics 314

5.5. Complete System of Equations for the Field of Steady Currents. Homogeneous Magnetic Medium 317

5.6. Mechanical Forces Acting on Currents in a Magnetic

Field. Interaction of Currents 319

5.7. Ponderomotive Forces Acting on Magnetics in a Magnetic Field 323

5.8. Supplement to the Derivation of the Macroscopic Equations for a

Magnetic Field in Magnetics 325

5.9. Mechanism of Magnetization of Magnetics. Larmor's Theorem 329

5.10. Diamagnetism 335

5.11. Paramagnetism 337

5.12. More Precise Definitions and Additions to the Theory of

Magnetization. The Part of Spin. Gyromagnetic Phenomena 343

5.13. Ferromagnetism. Weiss Molecular Field 348

5.14. Equations of the Field in Idealized Ferromagnetics (Conventional

Variant). Permanent Magnets 356

5.15. Another Variant of the Equations of the Magnetic Field in

Idealized Ferromagnetics. The Equivalence of Electric Currents and

Permanent Magnets 362

5.16. Ponderomotive Forces Acting on Permanent Magnets in an External Magnetic Field 371

6.

Quasistationary Electromagnetic Field 377

6.1. Induction of Currents in Moving Conductors 377

6.2. Law of Electromagnetic Induction. Ohm's Law for Varying Currents 382

6.3. Quasistationary Currents. Differential Equations for Varying

Currents 386

6.4. Transformations of Energy in the Field of Varying

Currents. Energy of Magnetic Interaction of Currents. Lenz's Law 389

6.5. Simple Applications of the Varying Current Theory. Transformer 395

6.6. Energy of a Magnetic Field. Energy Meaning of Inductances 403

6.7. Transformation of Energy in the Magnetization of Para- and Diamagnetics.

Free Energy of a Magnetic Field 411

6.8. Determination of the Ponderomotive Forces of a Magnetic Field

from the Expression for Energy 415

6.9. Stress Tensor of a Magnetic Field 421

6.10. Vortices of an Electric Field 424

6.11. Dependence of Electric Voltage on Integration Path. Voltage of Alternating Current 427

6.12. Equation of Continuity 432

6.13. Displacement Currents 434

6.14. A Capacitor in the Circuit of a Quasistationary Current. Electric Oscillations 441

6.15. The Skin Effect 446

7.

Varying Electromagnetic Field in a Stationary Medium and Its

Propagation. Electromagnetic Waves 455

7.1. System of Maxwell's Equations for Macroscopic Electromagnetic Field. 455

7.2. Poynting's Theorem. Energy Flow 461

7.3. Unambiguity of the Solutions of Maxwell's Equations 467

7.4. Differential Equations for the Potentials of an Electromagnetic Field 470

7.5. Solution of the Wave Equation and the d'Alembert Equation 474

7.6. Delayed and Advanced Potentials. Gauge Invariance 481

7.7. Velocity of Propagation of Electromagnetic Disturbances. Conditions for a Quasistationary State 488

7.8. Oscillator. Delayed Potentials of an Oscillator Field 492

7.9. Field of an Oscillator. Its Radiation 501

7.10. Electromagnetic Nature of Light. Plane Waves in a Dielectric 513

7.11. Reflection and Refraction of Plane Waves in Dielectrics 518

7.12. Propagation of Waves in a Conducting Medium. Reflection of Light

from a Metal Surface 527

7.13. Light Pressure. Momentum of an Electromagnetic Field 532

7.14. Electromagnetic Angular Momentum. A Particular Case of a Static

Field 539

7.15. Stress Tensor and Ponderomotive Forces of an Electromagnetic

Field 543

7.16. An Example of Non-Quasistationary Currents: Waves along a Cable 549

7.17. Approximate Theory of Fast-Varying Currents. "Telegraph Equation" 559

7.18. Free Energy of Ferromagnetics. Hysteresis 564

7.19. General Characteristic of the Theories of Short-Range and

Long-Range Interaction 571

8.

Electromagnetic Phenomena in Slowly Moving Media 576

8.1. Differential Equations of a Field in Moving Media 576

8.2. Convection Current. Polarization and Magnetization of Moving

Media 581

8.3. Ohm's Law and Electromagnetic Induction in Moving Conductors. Unipolar Induction 588

8.4. A Dielectric Moving in an Electromagnetic Field 595

8.5. Propagation of Light in Moving Dielectrics. Fresnel Drag

Coefficient. Reflection from a Moving Mirror 597

8.6. Transformations of Frame of Reference. Relative Nature of

Difference Between Electric and Magnetic Fields 602

9.

Appendix. Vector Analysis 608

A.1. Vector Algebra 608

A.2. Vector and Scalar Fields. Gradient 610

A.3. Vector Flux Through a Surface 616

A.4. Gauss's Theorem. Divergence 619

A.5. Circulation of a Vector. Curl of a Vector. Stokes's Theorem 626

A.6. Derivative of a Vector with Respect to Direction 634

A.7. The Nabla. Second Derivatives. Derivatives of a Product 635

A.8. Integral Relationships. Green's Theorem 642

A.9. The Most Important Formulas of Vector Analysis 645

Fundamental Formulas in the SI and Gaussian Systems of Units 648

Supplements 651

S.1. Superconductivity (to Sec. 3.7) 651

S.2. Antiferromagnetism and Ferrites (to Sec. 5.12) 651

S.3. Dispersive Media. Spatial Dispersion (to Sec. 7.2) 652

S.4. Anisotropic Media (to Sec. 7.2) 653

S.5. Vavilov-Cerenkov Effect (to Sec. 7.9) 654

S.6. Plasma (to Sec. 7.12) 654

Solutions of Problems 657

Name Index 673

Subject Index 674

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